• Arbitrary-order finite-Ttme corrections for the Kramers–Moyal operator 

      Gorjao, Leonardo; Witthaut, Dirk; Lehnertz, Klaus; Lind, Pedro (Peer reviewed; Journal article, 2021)
      : With the aim of improving the reconstruction of stochastic evolution equations from empirical time-series data, we derive a full representation of the generator of the Kramers–Moyal operator via a power-series expansion ...
    • Collective effects and synchronization of demand in real-time demand response 

      Han, Chengyuan; Witthaut, Dirk; Rydin Gorjao, Leonardo; Böttcher, Philipp (Journal of Physics: Complexity;Volume 3, Number 2, Peer reviewed; Journal article, 2022-04-28)
      Future energy systems will be dominated by variable renewable power generation and interconnected sectors, leading to rapidly growing complexity. Flexible elements are required to balance the variability of renewable power ...
    • Complexity and Persistence of Price Time Series of the European Electricity Spot Market 

      Han, Chengyuan; Hilger, Hannes; Mix, Eva; Böttcher, Philipp; Reyers, Mark; Beck, Christian; Witthaut, Dirk; Rydin Gorjao, Leonardo (PRX Energy;Vol. 1, Iss. 1 — April - June 2022, Peer reviewed; Journal article, 2022-04-07)
      The large variability of renewable power sources is a central challenge in the transition to a sustainable energy system. Electricity markets are central for the coordination of electric power generation. These markets ...
    • Data-driven model of the power-grid frequency dynamics 

      Rydin Gorjao, Leonardo; Anvari, Mehrnaz; Kantz, Holger; Beck, Christian; Witthaut, Dirk; Timme, Marc; Schäfer, Benjamin (IEEE Access;Volume 8, 2020, Peer reviewed; Journal article, 2020-01-20)
      The energy system is rapidly changing to accommodate the increasing number of renewable generators and the general transition towards a more sustainable future. Simultaneously, business models and market designs evolve, ...
    • jumpdiff: A Python Library for Statistical Inference of Jump-Diffusion Processes in Observational or Experimental Data Sets 

      Rydin Gorjão, Leonardo; Witthaut, Dirk; Lind, Pedro (Journal of Statistical Software;, Peer reviewed; Journal article, 2023)
      We introduce a Python library, called jumpdiff, which includes all necessary functions to assess jump-diffusion processes. This library includes functions which compute a set of non-parametric estimators of all contributions ...
    • Open database analysis of scaling and spatio-temporal properties of power grid frequencies 

      Rydin Gorjao, Leonardo; Jumar, Richard; Maass, Heiko; Hagenmeyer, Veit; Yalcin, G. Cigdem; Kruse, Johannes; Timme, Marc; Beck, Christian; Witthaut, Dirk; Schäfer, Benjamin (Peer reviewed; Journal article, 2020)
      The electrical energy system has attracted much attention from an increasingly diverse research community. Many theoretical predictions have been made, from scaling laws of fluctuations to propagation velocities of ...
    • Spatio-temporal complexity of power-grid frequency fluctuations 

      Rydin Gorjao, Leonardo; Schäfer, Benjamin; Witthaut, Dirk; Beck, Christian (Peer reviewed; Journal article, 2021)
      Power-grid systems constitute one of the most complex man-made spatially extended structures. These operate with strict operational bounds to ensure synchrony across the grid. This is particularly relevant for power-grid ...
    • Validation Methods for Energy Time Series Scenarios From Deep Generative Models 

      Cramer, Eike; Rydin Gorjao, Leonardo; Mitsos, Alexander; Schäfer, Benjamin; Witthaut, Dirk; Dahmen, Manuel (IEEE Access;Volume: 10, Peer reviewed; Journal article, 2022-01-11)
      The design and operation of modern energy systems are heavily influenced by time-dependent and uncertain parameters, e.g., renewable electricity generation, load-demand, and electricity prices. These are typically represented ...